Scholarlink

<p>In this paper, we investigate the initial-boundary value problems 3 × 3 system of two-phase flow. The phase interfaces in our system play a role similar to the contact discontinuities or entropy waves in full Euler equations. Even if considering the isothermal two-phase fluids, the existence of BV solutions in the large is a nontrivial issue. The effect of boundary together with steep phase interfaces probably results in the blow-up of weak solutions under large perturbations. Hence the conventional strategy of imposing weights on shock waves is invalid for boundary value problems. Based on more delicate Glimm-type estimates in present paper, we employ wave-front tracking algorithm to construct the global weak solutions under a wide class of large initial-boundary data. Concerning the total strengths of phase interfaces, our result improves the admissible range from (0, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({1 \over 2}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </math></EquationSource> </InlineEquation>) to (0,1).</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Existence of Global Solutions for the Initial-Boundary Value Problems of Two-Phase Flow Equations with Large Data

  • 期刊论文

  • 发表日期：

    2026年7月7日

查看全文
  • Kai Hu,
  • Shi-yi Wang

摘要

In this paper, we investigate the initial-boundary value problems 3 × 3 system of two-phase flow. The phase interfaces in our system play a role similar to the contact discontinuities or entropy waves in full Euler equations. Even if considering the isothermal two-phase fluids, the existence of BV solutions in the large is a nontrivial issue. The effect of boundary together with steep phase interfaces probably results in the blow-up of weak solutions under large perturbations. Hence the conventional strategy of imposing weights on shock waves is invalid for boundary value problems. Based on more delicate Glimm-type estimates in present paper, we employ wave-front tracking algorithm to construct the global weak solutions under a wide class of large initial-boundary data. Concerning the total strengths of phase interfaces, our result improves the admissible range from (0, \({1 \over 2}\) 1 2 ) to (0,1).